Statistics and Probability Answers

Determine the required probabilities.

Suppose you are to draw a ball from a box consisting of 2 red, 2 blue and 2 yellow balls twice.Let R be the random variable representing the number of Red. What is the probability of getting atleast 1 red?

consider tje population consisting of the value 1,3,4 list all the possible size2 that can be drawn from the population with replacement , compute the mean, variance and standard deviation of the sampling distribution of the means , construct the probability histogram of the sample mean with replacement when n=2

The table below shows data collected in a research on the relationship

between monthly income and monthly expenditure of citizens in town Q.

Use it to answer the following questions.

Earner A B C D E F G H I J

Income usd . 44 65 50 57 96 94 110 34 79 65

Expenditure usd.“ 41 60 40 50 80 68 84 30 55 48

(a) Fit the regression line of expenditure on income using least squares

method.

(b) Using the regression line obtained in (a) above, estimate the expected

amount of expenditure of a Kenyan whose monthly income is usd.

75,000.

For a group of 20 items, sum of X = 1452, sum of x ² = 144800 and mode = 67,

find the Karl Pearson’s coefficient of skewness and interpret the results.

2. A trader has 62 % chance of making a sale to each client. Given that the

behavior of successive clients is independent find the probability that the

trader will make a sale if two clients Lynn and Faith enter the trader’s

premises.

The results of the nationwide aptitude test in mathematics are normally distributed with a mean of 80 and a standard deviation of 15. Find the raw score such that 70% of the cases are below it.

The probability density function of a continuous random variable X is given below:

𝑓(𝑥) = {

1.25(1 − 𝑥

4

) , 0 < 𝑥 < 1

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

a. Find P(0.4< X<0.9)

b. Compute the expected value and variance of X.

If A and B are any two events defined on a sample space S with the following probabilities:   P(A)=0.44, P(B)=0.70, and P(A∩B)=0.44. Then, P(A∪B) is

Bag A contains 10 marbles of which 2 are red and 8 are black. Bag B contains 12 marbles of which 4 are red and 8 are black. A ball is drawn at random from each bag.

a) Draw a probability tree diagram to show all the outcomes the experiment.

b) find the probability that:

i. Both are red

ii. Both are black

iii) one black and one red

iv) at least one red

In a class of 40 students 15 grew cabbage 10 lettuce 5 both Cabbage and lettuce the rest neither calculate the probability that a randomly selected from class grew cabbage